getmode <- function(v) {
 uniqv <- unique(v)
 freq = max(tabulate(match(v, uniqv)))
 res = uniqv[which.max(tabulate(match(v, uniqv)))]
 if (freq == 1) res = NULL
 return(res)
}

d_central = data.frame(
  row.names = "Variable",
  Variable = c(
    "*ln(GDP)*",
    "*Sanitation*",
    "*Life Exp.*"
  ),
  Mean = c(
    mean(d$lngdp),
    mean(d$snt),
    mean(d$lfx)
  ),
  GM = c(
    geometric.mean(d$lngdp),
    geometric.mean(d$snt),
    geometric.mean(d$lfx)
  ),
  HM = c(
    harmonic.mean(d$lngdp),
    harmonic.mean(d$snt),
    harmonic.mean(d$lfx)
  ),
  Median = c(
    median(d$lngdp),
    median(d$snt),
    median(d$lfx)
  ),
  Mode = c(
    getmode(d$lngdp),
    getmode(d$snt),
    getmode(d$lfx)
  )
)

kable(
  d_central,
  col.names = c(
    "$\\bar{x}$",
    "$\\operatorname{GM}(x)$",
    "$\\operatorname{HM}(x)$",
    "$\\operatorname{median}(x)$",
    "$\\operatorname{mode}(x)$"
  ),
  digits=5
)

getmd = function(x, center = mean(x)){
  md = mean(
    abs(
      x - rep(center, length(x))
      )
    )
  return(md)
}
d_disp = data.frame(
  row.names = "Variable",
  Variable = c(
    "*ln(GDP)*",
    "*Sanitation*",
    "*Life Exp.*"
  ),
  Range = c(
    max(d$lngdp) - min(d$lngdp),
    max(d$snt) - min(d$snt),
    max(d$lfx) - min(d$lfx)
  ),
  SIR = c(
    IQR(d$lngdp)/2,
    IQR(d$snt)/2,
    IQR(d$lfx)/2
  ),
  MD = c(
    getmd(d$lngdp),
    getmd(d$snt),
    getmd(d$lfx)
  ),
  variance = c(
    (sd(d$lngdp))^2,
    (sd(d$snt))^2,
    (sd(d$lfx))^2
  ),
  SD = c(
    sd(d$lngdp),
    sd(d$snt),
    sd(d$lfx)
  )
)

kable(
  d_disp,
  col.names = c(
    "$\\operatorname{Range}(x)$",
    "$\\operatorname{SIR}(x)$",
    "$\\operatorname{MD}_{(\\bar{x})}(x)$",
    "$\\quad \\quad \\quad \\quad s_x^2$",
    "$\\quad \\quad \\quad \\quad s_x$"
  ),
  digits=5
)

labelfunction = function(val1){
  return(list(c(
    "log of GDP per capita",
    "Sanitation Access %",
    "Life Expectancy"
  )))
}
ggplot(stack(d[2:4]), mapping = aes(x = values))+
geom_density(aes(color=ind), linewidth=rel(1.5))+
labs(
  x=NULL,
  y=NULL
  )+
mytheme+
mycolor+
facet_wrap(~ind, scales="free", labeller = labelfunction, ncol=1)+
  theme(legend.position="none",
        strip.text.x = element_text(size = rel(1.5))
  )

labelfunction = function(val1){
  return(list(c(
    "log of GDP per capita",
    "Sanitation Access %",
    "Life Expectancy"
  )))
}
ggplot(stack(d[2:4]), mapping = aes(y = values))+
geom_boxplot(aes(fill=ind), alpha=0.6)+
labs(
  x=NULL,
  y=NULL
  )+
mytheme+
mycolor+
facet_wrap(~ind, scales="free", labeller = labelfunction)+
  theme(axis.text.x=element_blank(),
        legend.position="none",
        strip.text.x = element_text(size = rel(1.5)),
        panel.grid.minor.x = element_blank(),
        panel.grid.major.x = element_blank()
  )

olssmry = function(
    d, x_map, y_map,
    x_lab=waiver(), y_lab=waiver(),
    title=waiver()
){
  model = lm(formula=y_map~x_map)
  smry = summary(model, signif.stars=TRUE)
  
  smryvec = c(
    as.numeric(model$coefficients["(Intercept)"]),
    as.numeric(model$coefficients["x_map"]),
    smry$r.squared
  )
  
  return(smryvec)
}

olstab = t(data.frame(
  SvG = olssmry(d, d$lngdp, d$snt),
  LvG = olssmry(d, d$lngdp, d$lfx),
  LvS = olssmry(d, d$snt, d$lfx)
))

row.names(olstab) = c(
  "*Sanitation vs. ln(GDP)*",
  "*Life Exp. vs. ln(GDP)*",
  "*Life Exp. vs. Sanitation*"
)

kable(
  olstab,
  digit = 5,
  col.names=c(
  "$\\hat{a}$",
  "$\\hat{b}$",
  "$R^2$"
  )
)